Derrick Henry added 113 yards and another score on 17 attempts for the Crimson Tide (1-0), while Blake Sims ended up 24-of-33 for 250 yards and one interception.
Amari Cooper led all receivers with 12 receptions and racked up 130 yards for Alabama, which is seeking a third national title in the last four seasons.
Clint Trickett ended up 29-of-45 for 365 yards and a TD pass to Kevin White for the Mountaineers (0-1).
White collected 143 yards on nine grabs, while Mario Alford returned a kick 100 yards while adding 54 yards on five catches.
Adam Griffith's 41-yard boot on the final play of the first half gave Alabama a 20-17 edge, and though Sims came up short on a 4th-and-6 pass to Cooper on the first series of the second half, Josh Lambert missed a subsequent 47-yard try for West Virginia.
Alabama needed just six plays to gain some breathing room, as Henry's 19-yard scamper close to the midway point of the third provided a 27-17 margin.
Lambert connected from 42 yards away and the Mountaineers got back within 27-20 with 4:59 left in the period, but Griffith converted a 27-yarder to wrap up the ensuing possession and the Tide's lead was back up to 10.
The Mountaineers then had Alabama backed up deep in their own zone, but a bad snap on 3rd-and-goal from the 5-yard line forced Trickett to fall on the ball at the 24. Lambert, though, was good from 41 yards away and it was a seven- point game once more with 13:37 to go.
The Crimson Tide defense forced a three-and-out, then another make by Griffith -- this one from 45 yards out -- boosted Alabama's advantage to 10 points at 33-23.
WVU punted on the following series then Trickett's pass to Rushel Shell on 4th-and-11 late in the contest fell incomplete.
West Virginia made the most of its first drive, taking the early lead as Lambert converted from 20 yards away. Griffith capped Alabama's second possession with a 47-yard make.
A leap along the right sideline to cap a 15-yard dash by Yeldon capped a 95- yard drive and sent Alabama up 10-3 less than a minute into the second quarter.
The Mountaineers countered on their next series, when White beat a defender and came down in the back of the end zone with a lob from Trickett for a 19- yard score.
Yeldon then found the end zone from one yard out inside of two minutes left in the half, and the Tide regained the lead. However, it took Alford mere seconds to tie the game with a 100-yard return of the ensuing kickoff.
Alabama has won its last 13 season openers, and improved to 21-2 in such contests dating back to 1991 ... The Mountaineers saw their string of 10 consecutive season-opening victories snapped ... Shell led WVU with 38 yards on 10 carries ... The Crimson Tide rolled to 288 rushing yards, while their defense limited West Virginia to 28 yards on the ground on 24 attempts.